President Donald Trump said on Tuesday he's not looking to reinstate the much-criticised practice of separating migrant families at the border with Mexico. But he says many more migrants are streaming toward the US through Mexico because the practice is no longer in place.

Says Trump: "I'm the one that stopped it." He claims his predecessor, President Barack Obama, is the one who separated children from their families.

Trump ended the practice under pressure last year after footage of scores of migrant children housed in fenced-off cages at border facilities was broadcast widely. Trump's allies are pressing for a harder line on immigration after he cleaned house at the Homeland Security Department.

Trump says "once you don't have it", meaning the family separation policy, "that's why you see many more people coming".